Adaptive resolution simulation in equilibrium and beyond

In this paper, we investigate the equilibrium statistical properties of both the force and potential interpolations of adaptive resolution simulation (AdResS) under the theoretical framework of grand-canonical like AdResS (GC-AdResS). The thermodynamic relations between the higher and lower resolutions are derived by considering the absence of fundamental conservation laws in mechanics for both branches of AdResS. In order to investigate the applicability of AdResS method in studying the properties beyond the equilibrium, we demonstrate the accuracy of AdResS in computing the dynamical properties in two numerical examples: The velocity auto-correlation of pure water and the conformational relaxation of alanine dipeptide dissolved in water. Theoretical and technical open questions of the AdResS method are discussed in the end of the paper.